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In a class of 78 students 41 are taking French, 22 are takin
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01 Feb 2018, 21:32
01 Feb 2018, 21:32
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Question Stats:
93% (00:58) correct
6% (01:11) wrong based on 74 sessions
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In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A)6
B)15
C)24
D)33
E)54
A)6
B)15
C)24
D)33
E)54
Sherpa Prep Representative
Joined: 15 Jan 2018
Posts: 147
Given Kudos: 0
Re: In a class of 78 students 41 are taking French, 22 are takin
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Updated on: 04 Feb 2018, 22:07
Updated on: 04 Feb 2018, 22:07
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Expert Reply
This is a double overlapping set. Venn diagrams are OK for these but can be confusing. There's an equation as well, but the best way to solve these is to use an Overlapping Sets Matrix. Just make a matrix with French and Not French, German and Not German, and fill in the boxes that they give you. See first attachment.
Then you can fill in the empty boxes until you get the answer you want. Since the students studying both languages and the students studying only German must add up to the total learning German, you can fill in the blank in between them. And in every row and column, if you have two filled in, you can fill in the third. See second attachment.
So, the answer is 24.
Then you can fill in the empty boxes until you get the answer you want. Since the students studying both languages and the students studying only German must add up to the total learning German, you can fill in the blank in between them. And in every row and column, if you have two filled in, you can fill in the third. See second attachment.
So, the answer is 24.
Attachments
French and German.jpg [ 31.8 KiB | Viewed 13271 times ]
French and German complete.jpg [ 34.74 KiB | Viewed 13331 times ]
Originally posted by SherpaPrep on 01 Feb 2018, 23:18.
Last edited by SherpaPrep on 04 Feb 2018, 22:07, edited 1 time in total.
Last edited by SherpaPrep on 04 Feb 2018, 22:07, edited 1 time in total.
Re: In a class of 78 students 41 are taking French, 22 are takin
[#permalink]
02 Feb 2018, 02:38
02 Feb 2018, 02:38
1
SherpaPrep wrote:
This is a double overlapping set. Venn diagrams are OK for these but can be confusing. There's an equation as well, but the best way to solve these is to use an Overlapping Sets Matrix. Just make a matrix with French and Not French, German and Not German, and fill in the boxes that they give you. See first attachment.
Then you can fill in the empty boxes until you get the answer you want. Since the students studying both languages and the students studying only German must add up to the total learning German, you can fill in the blank in between them. And in every row and column, if you have two filled in, you can fill in the third. See second attachment.
So, the answer is 22.
Then you can fill in the empty boxes until you get the answer you want. Since the students studying both languages and the students studying only German must add up to the total learning German, you can fill in the blank in between them. And in every row and column, if you have two filled in, you can fill in the third. See second attachment.
So, the answer is 22.
The question asks for those that are not enrolled in either courses so from the double-matrix diagram the number that should give the ans is those that are not enrolled in German and Those that are not enrolled in French = 24.
